The worldwide fleet of Boeing 787 Dreamliners has been grounded due to problems with the aircraft’s electrical power and distribution systems, but with only six of the jets in service in the United States, you might think the problem isn't too bad.

You'd be wrong. While the long-range, mid-size jet isn't in heavy use yet, the repercussions of this grounding will be felt across the aerospace industry.

The Dreamliner's troubles began with an incident in Boston on January 7, when a battery on an empty 787 caught fire. On January 11, the FAA ordered a comprehensive review of the 787’s critical systems. But on January 16 another Dreamliner was forced to make an emergency landing after on-board alarms indicated smoke in an electrical compartment, and passengers reported a burning smell in the cabin.

As a result, the FAA issued an emergency airworthiness directive requiring that operators of U.S.-registered Boeing 787 aircraft temporarily cease operations, and demonstrate that the Dreamliner's batteries are safe before resuming operations.

"The AD is prompted by this second incident involving a lithium ion battery," the FAA said in a statement. "The battery failures resulted in release of flammable electrolytes, heat damage, and smoke on two Model 787 airplanes. The root cause of these failures is currently under investigation. These conditions, if not corrected, could result in damage to critical systems and structures, and the potential for fire in the electrical compartment."

Because the Dreamliner's problems appear to be a complex issue involving entire electrical subsystems, it could take months to complete an investigation into the Dreamliner's problems and get the jets back into the air.

"We are confident the 787 is safe and we stand behind its overall integrity," Boeing CEO Jim McNerney said in a statement after the directive went into effect. "We will be taking every necessary step in the coming days to assure our customers and the traveling public of the 787's safety and to return the airplanes to service."

The grounding may be most obviously bad news for Boeing, but the damage will be spread far beyond the Seattle aerospace giant.

The only U.S. airline immediately affected by the directive is United Airlines, which flies six of the affected 787s. United has already switched out the jets with similar-sized Boeing 767s, and all the flight delays caused by the swap appear to have worked their way out of the system. But United has 44 more Dreamliners on order, so an extended grounding --or any evidence that this is a larger systemic problem-- could cause problems in the future. The same goes for several other U.S. companies -- American Airlines recently ordered 42 Dreamliners, Delta Air Lines has 18 of the jets on order, and several leasing companies also have outstanding orders, including AIG.

After grounding their two Dreamliners, the chief of the Polish national airline LOT said he will seek compensation from Boeing for the "huge" costs caused by keeping the jets grounded, and review the planned delivery of three more of the aircraft which were due in the next two months.

"We are analysing our contract with Boeing from the perspective of our possibilities of filing for compensation," Tomasz Balcerzak said in a press conference. "All elements and irregularities that generate cost mean that we will file for compensation in due time."

And Boeing isn't the only company at risk here: Companies that manufacture affected parts of the Dreamliner's electrical systems are also on the hot seat, including United Technologies, the Thales Group, and Japan's GS Yuasa Corporation, which makes the Dreamliner's batteries.

So far, the markets have been relatively kind to affected companies: Shares of Boeing stock closed up 1.24% at $75.26 on Thursday, and are down less than a percentage point since the beginning of January.